Deformations of a thick-valued, slowly rotating cylinder under gravitational load

Abstract

An analytic method of calculating the deformations of an infinitely long thick-walled cylinder under a periodically varying gravitational load is described. The cylinder material is linearly viscoelastic. The solution employs the elasto-viscoelastic analogy. The corresponding elastic problem is solved by Muskhelishvili's method. The nonhomogeneity of the equilibrium equations is eliminated by applying the theorem of body forces with a potential function. As an example the maximum displacements of the inner channel are calculated for a cylinder of incompressible material in the cases of slow continuous rotation and periodic rotation through 180°.